MATH SOLVE

3 months ago

Q:
# Jimmy owns a small engine repair business. The revenue, in dollars, can be modeled by the equation y = 420 + 72x, where x is the number of hours spent repairing small engines. The overhead cost, in dollars, can be modeled by the equation y = 24x² + 180 where x is the number of hours spent repairing bikes.After about how many hours does the company break even?Note: The phrase break even refers to the value where the two functions are equivalent.1 h5 h2 h10 h

Accepted Solution

A:

Answer:5 hoursStep-by-step explanation:Given[tex]y = 420 + 72x[/tex] --- Revenue[tex]y = 24x^2 + 180[/tex] --- Overhead costRequiredDetermine the hours for break evenTo do this, we simply equate both expressions as follows:[tex]24x^2 + 180 = 420 + 72x[/tex]Collect Like Terms[tex]24x^2 - 72x + 180 - 420 = 0[/tex][tex]24x^2 - 72x -240 = 0[/tex]Divide through 24[tex]x^2 - 3x - 10 = 0[/tex]Expand:[tex]x^2 -5x + 2x -10 = 0[/tex]Factorize:[tex]x(x -5) + 2(x -5) = 0[/tex][tex](x + 2)(x -5) = 0[/tex][tex]x + 2 = 0\ or\ x - 5 = 0[/tex][tex]x = -2\ or\ x = 5[/tex]But x can't be negative because it represents time.So, x = 5 hours